Abstract

It is shown that a novel class of optical solitons is possible in nonlinear dispersive media with birefringence.

© 1988 Optical Society of America

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References

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  1. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  2. D. N. Christodoulides, R. I. Joseph, Electron. Lett. 20, 659 (1984).
    [CrossRef]
  3. A. E. Kaplan, C. T. Law, IEEE J. Quantum Electron. QE-21, 1529 (1985).
    [CrossRef]
  4. H. G. Winful, Appl. Phys. Lett. 47, 213 (1985); Opt. Lett. 11, 33 (1986).
    [CrossRef] [PubMed]
  5. S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986); B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986).
    [CrossRef] [PubMed]
  6. A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).
  7. S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).
  8. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  9. C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
    [CrossRef]
  10. P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
    [CrossRef]
  11. K. J. Blow, N. J. Doran, D. Wood, Opt. Lett. 12, 202 (1987).
    [CrossRef] [PubMed]
  12. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, New York, 1983); K. Okamoto, T. Hosaka, Opt. Lett. 12, 290 (1987).
    [CrossRef] [PubMed]
  13. L. D. Landau, E. M. Lifshitz, Mechanics (Pergamon, Oxford, 1960). In Eq. (6) and thereafter, the velocities x˙ and y˙ involved in the Hamiltonians implicitly represent the momenta px and py, respectively.
  14. H. Grosse, Acta Phys. Austr. 52, 89 (1980); J. Hietarinta, Phys. Lett. A 96, 273 (1983).
    [CrossRef]
  15. J. Kay, H. E. Moses, J. Appl. Phys. 27, 1503 (1956); Y. Nogami, C. S. Warke, Phys. Lett. A 59, 251 (1976).
    [CrossRef]
  16. T. Bountis, H. Segur, F. Vivaldi, Phys. Rev. A 25, 1257 (1982).
    [CrossRef]
  17. R. Friedberg, T. D. Lee, A. Sirlin, Phys. Rev. D 13, 2739 (1976).
    [CrossRef]
  18. W. H. Steeb, J. A. Louw, Chaos and Quantum Chaos (World Scientific, Philadelphia, Pa., 1986).
  19. S. G. Matinyan, G. K. Savvidi, N. G. Savvidi, JETP Lett. 34, 590 (1981).

1987 (2)

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[CrossRef]

K. J. Blow, N. J. Doran, D. Wood, Opt. Lett. 12, 202 (1987).
[CrossRef] [PubMed]

1986 (1)

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986); B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986).
[CrossRef] [PubMed]

1985 (2)

A. E. Kaplan, C. T. Law, IEEE J. Quantum Electron. QE-21, 1529 (1985).
[CrossRef]

H. G. Winful, Appl. Phys. Lett. 47, 213 (1985); Opt. Lett. 11, 33 (1986).
[CrossRef] [PubMed]

1984 (1)

D. N. Christodoulides, R. I. Joseph, Electron. Lett. 20, 659 (1984).
[CrossRef]

1982 (1)

T. Bountis, H. Segur, F. Vivaldi, Phys. Rev. A 25, 1257 (1982).
[CrossRef]

1981 (1)

S. G. Matinyan, G. K. Savvidi, N. G. Savvidi, JETP Lett. 34, 590 (1981).

1980 (2)

H. Grosse, Acta Phys. Austr. 52, 89 (1980); J. Hietarinta, Phys. Lett. A 96, 273 (1983).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1976 (1)

R. Friedberg, T. D. Lee, A. Sirlin, Phys. Rev. D 13, 2739 (1976).
[CrossRef]

1974 (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

1972 (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

1970 (1)

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

1964 (1)

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

1956 (1)

J. Kay, H. E. Moses, J. Appl. Phys. 27, 1503 (1956); Y. Nogami, C. S. Warke, Phys. Lett. A 59, 251 (1976).
[CrossRef]

Assanto, G.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986); B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986).
[CrossRef] [PubMed]

Berkhoer, A. L.

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

Blow, K. J.

Bountis, T.

T. Bountis, H. Segur, F. Vivaldi, Phys. Rev. A 25, 1257 (1982).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides, R. I. Joseph, Electron. Lett. 20, 659 (1984).
[CrossRef]

Doran, N. J.

Friedberg, R.

R. Friedberg, T. D. Lee, A. Sirlin, Phys. Rev. D 13, 2739 (1976).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Grosse, H.

H. Grosse, Acta Phys. Austr. 52, 89 (1980); J. Hietarinta, Phys. Lett. A 96, 273 (1983).
[CrossRef]

Joseph, R. I.

D. N. Christodoulides, R. I. Joseph, Electron. Lett. 20, 659 (1984).
[CrossRef]

Kaplan, A. E.

A. E. Kaplan, C. T. Law, IEEE J. Quantum Electron. QE-21, 1529 (1985).
[CrossRef]

Kay, J.

J. Kay, H. E. Moses, J. Appl. Phys. 27, 1503 (1956); Y. Nogami, C. S. Warke, Phys. Lett. A 59, 251 (1976).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Mechanics (Pergamon, Oxford, 1960). In Eq. (6) and thereafter, the velocities x˙ and y˙ involved in the Hamiltonians implicitly represent the momenta px and py, respectively.

Law, C. T.

A. E. Kaplan, C. T. Law, IEEE J. Quantum Electron. QE-21, 1529 (1985).
[CrossRef]

Lee, T. D.

R. Friedberg, T. D. Lee, A. Sirlin, Phys. Rev. D 13, 2739 (1976).
[CrossRef]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Mechanics (Pergamon, Oxford, 1960). In Eq. (6) and thereafter, the velocities x˙ and y˙ involved in the Hamiltonians implicitly represent the momenta px and py, respectively.

Louw, J. A.

W. H. Steeb, J. A. Louw, Chaos and Quantum Chaos (World Scientific, Philadelphia, Pa., 1986).

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, New York, 1983); K. Okamoto, T. Hosaka, Opt. Lett. 12, 290 (1987).
[CrossRef] [PubMed]

Maker, P. D.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Manakov, S. V.

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Matinyan, S. G.

S. G. Matinyan, G. K. Savvidi, N. G. Savvidi, JETP Lett. 34, 590 (1981).

Menyuk, C. R.

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Moses, H. E.

J. Kay, H. E. Moses, J. Appl. Phys. 27, 1503 (1956); Y. Nogami, C. S. Warke, Phys. Lett. A 59, 251 (1976).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Savvidi, G. K.

S. G. Matinyan, G. K. Savvidi, N. G. Savvidi, JETP Lett. 34, 590 (1981).

Savvidi, N. G.

S. G. Matinyan, G. K. Savvidi, N. G. Savvidi, JETP Lett. 34, 590 (1981).

Seaton, C. T.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986); B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986).
[CrossRef] [PubMed]

Segur, H.

T. Bountis, H. Segur, F. Vivaldi, Phys. Rev. A 25, 1257 (1982).
[CrossRef]

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Sirlin, A.

R. Friedberg, T. D. Lee, A. Sirlin, Phys. Rev. D 13, 2739 (1976).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, New York, 1983); K. Okamoto, T. Hosaka, Opt. Lett. 12, 290 (1987).
[CrossRef] [PubMed]

Steeb, W. H.

W. H. Steeb, J. A. Louw, Chaos and Quantum Chaos (World Scientific, Philadelphia, Pa., 1986).

Stegeman, G. I.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986); B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986).
[CrossRef] [PubMed]

Stolen, R. H.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986); B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Trillo, S.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986); B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986).
[CrossRef] [PubMed]

Vivaldi, F.

T. Bountis, H. Segur, F. Vivaldi, Phys. Rev. A 25, 1257 (1982).
[CrossRef]

Wabnitz, S.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986); B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986).
[CrossRef] [PubMed]

Winful, H. G.

H. G. Winful, Appl. Phys. Lett. 47, 213 (1985); Opt. Lett. 11, 33 (1986).
[CrossRef] [PubMed]

Wood, D.

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

Acta Phys. Austr. (1)

H. Grosse, Acta Phys. Austr. 52, 89 (1980); J. Hietarinta, Phys. Lett. A 96, 273 (1983).
[CrossRef]

Appl. Phys. Lett. (2)

H. G. Winful, Appl. Phys. Lett. 47, 213 (1985); Opt. Lett. 11, 33 (1986).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986); B. Daino, G. Gregori, S. Wabnitz, Opt. Lett. 11, 42 (1986).
[CrossRef] [PubMed]

Electron. Lett. (1)

D. N. Christodoulides, R. I. Joseph, Electron. Lett. 20, 659 (1984).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. E. Kaplan, C. T. Law, IEEE J. Quantum Electron. QE-21, 1529 (1985).
[CrossRef]

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987).
[CrossRef]

J. Appl. Phys. (1)

J. Kay, H. E. Moses, J. Appl. Phys. 27, 1503 (1956); Y. Nogami, C. S. Warke, Phys. Lett. A 59, 251 (1976).
[CrossRef]

JETP Lett. (1)

S. G. Matinyan, G. K. Savvidi, N. G. Savvidi, JETP Lett. 34, 590 (1981).

Opt. Lett. (1)

Phys. Rev. A (1)

T. Bountis, H. Segur, F. Vivaldi, Phys. Rev. A 25, 1257 (1982).
[CrossRef]

Phys. Rev. D (1)

R. Friedberg, T. D. Lee, A. Sirlin, Phys. Rev. D 13, 2739 (1976).
[CrossRef]

Phys. Rev. Lett. (2)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Sov. Phys. JETP (3)

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other (3)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, New York, 1983); K. Okamoto, T. Hosaka, Opt. Lett. 12, 290 (1987).
[CrossRef] [PubMed]

L. D. Landau, E. M. Lifshitz, Mechanics (Pergamon, Oxford, 1960). In Eq. (6) and thereafter, the velocities x˙ and y˙ involved in the Hamiltonians implicitly represent the momenta px and py, respectively.

W. H. Steeb, J. A. Louw, Chaos and Quantum Chaos (World Scientific, Philadelphia, Pa., 1986).

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Figures (1)

Fig. 1
Fig. 1

Field profiles of the x(τ) and y(τ) components in the normalized time domain τ for η1 = 0.5 and η2 = 1. The solid curve represents x(τ), and the dashed curve represents y(τ).

Equations (15)

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P NL = χ ( 3 ) [ A E ( E · E * ) + B E * ( E · E ) ] ,
i u z + 1 2 2 u τ 2 + ( | u | 2 + A | υ | 2 ) u + B υ 2 u * exp ( 4 iκz ) = 0 , i υ z + 1 2 2 υ τ 2 + ( | υ | 2 + A | u | 2 ) υ + B u 2 υ * exp ( + 4 iκz ) = 0 ,
z [ d τ ( | u | 2 + | υ | 2 ) ] = 0 ,
u = x ( τ ) exp [ i ( μ + κ ) z ] , υ = y ( τ ) exp [ i ( μ κ ) z ] ,
x ¨ + 2 ( μ + κ ) x + 2 ( x 2 + y 2 ) x = 0 , y ¨ + 2 ( μ κ ) y + 2 ( x 2 + y 2 ) y = 0 ,
H = x ˙ 2 + y ˙ 2 2 + ( μ + κ ) x 2 + ( μ κ ) y 2 + 1 2 ( x 2 + y 2 ) 2 .
H = r ˙ 2 2 + l 2 2 r 2 + μ r 2 + r 4 2 .
x = r 0 sech ( r 0 τ ) cos θ 0 , y = r 0 sech ( r 0 τ ) sin θ 0 ,
x = η 1 [ cosh ( η 2 τ ) η 2 η 1 + η 2 exp ( η 2 τ ) ] { cosh ( η 1 τ ) cosh ( η 2 τ ) η 1 η 2 ( η 1 + η 2 ) 2 exp [ ( η 1 + η 2 ) τ ] } , y = η 2 [ cosh ( η 2 τ ) η 2 η 1 + η 2 exp ( η 1 τ ) ] { cosh ( η 1 τ ) cosh ( η 2 τ ) η 1 η 2 ( η 1 + η 2 ) 2 exp [ ( η 1 + η 2 ) τ ] } ,
u = B 1 / 2 2 q 1 ( τ ) exp [ i ( μ + κ ) z ] , υ = i B 1 / 2 2 q 2 ( τ ) exp [ i ( μ κ ) z ] .
q ¨ 1 + 2 ( μ + κ ) q 1 + ( 2 σ + 1 ) 2 q 1 3 + ( 2 σ 1 ) 2 q 1 q 2 2 = 0 , q ¨ 2 + 2 ( μ κ ) q 2 + ( 2 σ + 1 ) 2 q 2 3 + ( 2 σ 1 ) 2 q 1 2 q 2 = 0 ,
H = q ˙ 1 2 + q ˙ 2 2 4 + ( μ + κ ) 2 q 1 2 + ( μ κ ) 2 q 2 2 + ( 2 σ + 1 ) 16 ( q 1 4 + q 2 4 ) + ( 2 σ 1 ) 8 q 1 2 q 2 2 .
q 1 = 2 1 / 2 η 1 sech ( η 1 τ ) , q 2 = 2 1 / 2 η 2 sech ( η 2 τ ) ,
H = P ˙ 1 2 + P ˙ 2 2 2 + μ ( P 1 2 + P 2 2 ) + 2 κ P 1 2 P 2 2 + σ 2 ( P 1 4 + P 2 4 ) + ( σ + 1 ) P 1 2 P 2 2 .
P ˙ 1 P ˙ 2 + ( P 1 P 2 + κ ) ( P 1 2 + P 2 2 ) + 2 μ P 1 P 2 = const .,

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